Boron Neutron Capture Therapy (BNCT) of brain tumors is in clinical trials at BNL using a filtered beam from the Medical Reactor. Unfortunately, there are few available reactors in the U. S. which could be used to provide treatment, especially near existing hospitals, and little prospect of constructing new ones, particularly near large population centers. If a small proton accelerator to produce the neutrons is found to be acceptable, then BNCT could become a readily available clinical procedure since the difficulties in siting would be greatly reduced. This study will investigate the feasibility of producing neutrons for BNCT with an accelerator rather than with a reactor. The major emphasis is the design of the targets used to produce the neutrons and moderator designs to optimize the neutron yield and energy spectrum and to minimize the dose contribution from gamma rays.